Smell of burning?

You don't say if the motor works normaly, or just emit a low humm.

Over heating is a sign of a jammed motor or blocked air flow, not a faulty belt.

Check that the motor spin normaly. While unplugged, hold the power cable's plug in your hand, manualy turn the motor. It should turn easily.

Look if there is any dust accumulation in it. If there is dust accumulation, remove as much of it as you can. Dust, and any other obstruction, can prevent air flow to the motor and cause it to overheat.

After a prolonged un-use period, there may be some rusting, especialy if it was stored in a somewhat humid environment. Put a very small amount of light oil on the bearings. Rotate the motor's rotor by hand. Plug the vacuum in and turn it on. The motor must spin freely. Unplug and whip out any excess oil. You don't want oily surfaces to catch any dust.

Electro
January 2012